Question

The acceleration of a 5 kg object is described below: from time t = 0 to t = 10 seconds, the acceleration is constant and given by the following formula: a = 6 m/s^2. From time t = 10 - 20 second, the acceleration is no longer constant, but is time dependent and is given by the formula a = (0.3 m/s^3)t +3 m/s^2 produce a single graph of force vs. time in excel that illustrates this. Your data should start at t = 0 and go up to t= 20 seconds in increments of .1 seconds. B. calculate the impulse from the graph

Answer 1

Here, the acceleration at different times is known.

We have to draw force-time graph.

The force is given by

F = m*a

Here, m = 5 kg.

First, we have to make a table in excel, with one column time in steps of 1 from 1 to 20 seconds, and another column force.

Time (s)	Acceleration	Force (N)
0	6	30
1	6	30
2	6	30
3	6	30
4	6	30
5	6	30
6	6	30
7	6	30
8	6	30
9	6	30
10	6	30
11	6.3	31.5
12	6.6	33
13	6.9	34.5
14	7.2	36
15	7.5	37.5
16	7.8	39
17	8.1	40.5
18	8.4	42
19	8.7	43.5
20	9	45

With this, we can draw a scatter plot.

b) The impulse is the area under the graph.

Impulse = Area of the rectangular region + area of the triangular region.

Impulse = 30*20 + (1/2)*15*10 = 675 Ns .